Theme Essential Question: How can you use geometric formulas to solve real-world and mathematical problems?
Essential Questions: How do you find the volume of a figure made up of cubes and prisms?
Standards:
7. G. 6 Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Objectives:
The student will solve real-world and mathematical problems involving volumes dealing with cubes.
The student will solve real-world and mathematical problems involving volume of right prisms.
The student will solve real-world and mathematical problems involving composite solids.
The student will cultivate an understanding of volume as it is associated to unit cubes and the area of the base of the prism.
Background: Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials athttp://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022 Real-world and mathematical multi-step problems that require finding area, perimeter, volume, surface area of figures composed of triangles, quadrilaterals, polygons, cubes and right prisms should reflect situations relevant to seventh graders. The computations should make use of formulas and involve whole numbers, fractions, decimals, ratios and various units of measure with same system conversions.
Assessment: Product:
ZOO TRAINER project continues:
The stable and feed storage areas will be cooled by using a special air-circulation system. Determine the volume that the special air-circulation system must handle. Prepare detail documentation of your calculations.
Key Questions
How does the study of cubes related to the calculation of volumes?
What is the meaning of cubic units?
How does the formula for a rectangular prism LxWxH relate to the basic formula for all prisms BxH?
Observable Student Behaviors (Performance)
The student can find surface area of prisms.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Cubes Volume
Suggested Activities:
Houghton Mifflin OnCore Mathematics Middle School Grade 7
Unit 5-5, p. 127-130
Unit 5 Test Prep, p. 135-136
ABC Mastering the Common Core in Mathematics
Chapter 13.3, Understanding Volume, p. 162
Chapter 13.4, Volume of Cubes and Rectangular Prisms, p. 162
Chapter 13.5, Volume of Other Prisms, p. 165
Chapter 13.6, Volume of Pyramids (extension), p. 167
Chapter Review and test, p 173
Gizmo Correlation:
Balancing Blocks (Volume)
This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. (Student Exploration Sheet & Teacher Guide Available)
Prisms and Cylinders-Activity A
Vary the height and base edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew prism or cylinder to the volume of a right prism or cylinder.
Teaching the Common Core Math Standards with Hands-On Activities,
7.G.6, Activity: Let’s Build It, p. 127-128
Highly Recommended: http://illustrativemathematics.org/illustrations/266 (G.6) The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 8th, GP 1, p. 325-342
Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 12-2, p. 520-521
Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Students will practice finding the Circumference, Volume, and Surface Area of given shapes/figures
7.G. 6 Surface Area of Prisms
This lesson will help the students with the formula for lateral area of a prism
7.G. 6 Should I Cover It Up…Or Go Around It?
While looking at geometric shapes in sports, students wll determine whether to find the area or the perimeter for each problem set before them. I have included a football field and a basketball court for challenges. Some sildes require more higher level of learning and more challenging Bloom's Taxonomy questions.
7.G. 6 Measurement Part 1: Area
This lesson activity provides introduces and provides practice in calculating the area of various shapes.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Content: Solving Volume Problems
Dates: 3/4/2013 – 3/8/2013
Theme Essential Question:
How can you use geometric formulas to solve real-world and mathematical problems?
Essential Questions:
How do you find the volume of a figure made up of cubes and prisms?
Standards:
Objectives:
Background:
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials athttp://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Real-world and mathematical multi-step problems that require finding area, perimeter, volume, surface area of figures composed of triangles, quadrilaterals, polygons, cubes and right prisms should reflect situations relevant to seventh graders. The computations should make use of formulas and involve whole numbers, fractions, decimals, ratios and various units of measure with same system conversions.
Assessment:
Product:
- ZOO TRAINER project continues:
The stable and feed storage areas will be cooled by using a special air-circulation system.Determine the volume that the special air-circulation system must handle. Prepare detail documentation of your calculations.
Key Questions
Observable Student Behaviors (Performance)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Suggested Activities:
- Houghton Mifflin OnCore Mathematics Middle School Grade 7
- Unit 5-5, p. 127-130
- Unit 5 Test Prep, p. 135-136
- ABC Mastering the Common Core in Mathematics
- Chapter 13.3, Understanding Volume, p. 162
- Chapter 13.4, Volume of Cubes and Rectangular Prisms, p. 162
- Chapter 13.5, Volume of Other Prisms, p. 165
- Chapter 13.6, Volume of Pyramids (extension), p. 167
- Chapter Review and test, p 173
- Gizmo Correlation:
- Balancing Blocks (Volume)
This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. (Student Exploration Sheet & Teacher Guide Available)- Prisms and Cylinders-Activity A
Vary the height and base edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew prism or cylinder to the volume of a right prism or cylinder.- Teaching the Common Core Math Standards with Hands-On Activities,
- 7.G.6, Activity: Let’s Build It, p. 127-128
Highly Recommended:http://illustrativemathematics.org/illustrations/266 (G.6)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
- JBHM 8th, GP 1, p. 325-342
- Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 12-2, p. 520-521
- Glencoe Pre-Algebra, Chapter 11-2, p. 563-567
- Glencoe Algebra I, Chapter 8, p. 416
- Create a puzzle with unit vocabulary words.
http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576Diverse Learners
Homework: (Teachers Discretion)
Terminology for Teachers:
Resources:
Professional Texts:
Literary Texts:
- Geometry and Literature Titles:
http://sci.tamucc.edu/~eyoung/geometry_literature.html- Measurement and children’s Literature/Ratios
http://sci.tamucc.edu/~eyoung/measure_literature.html- Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music and Media
Manipulatives:
Games
Videos
SMART Board Lessons, Promethean Lessons
- Smart Board rational number lessons
http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2ea- Rational numbers Smart Board lessons
http://exchange.smarttech.com/details.html?id=050e54ad-0dea-4080-ae54-975d93487209- 7.G. 6 Circumference, Volume, Surface Area
Students will practice finding the Circumference, Volume, and Surface Area of given shapes/figures- 7.G. 6 Surface Area of Prisms
This lesson will help the students with the formula for lateral area of a prism- 7.G. 6 Should I Cover It Up…Or Go Around It?
While looking at geometric shapes in sports, students wll determine whether to find the area or the perimeter for each problem set before them. I have included a football field and a basketball court for challenges. Some sildes require more higher level of learning and more challenging Bloom's Taxonomy questions.- 7.G. 6 Measurement Part 1: Area
This lesson activity provides introduces and provides practice in calculating the area of various shapes.Other Activities, etc.
- Puzzle Maker
- http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Activities and tools:
http://www.shodor.org/interactivate/activities/
Language
Arts
Week 1
Week 2
Week 3
Week 4
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4